Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Dec 21 2021 10:15:26
%S 1,2,3,1,4,2,5,3,1,1,6,4,7,5,2,2,8,6,9,7,3,3,10,8,4,4,1,1,11,9,12,10,
%T 5,5,2,2,13,11,6,6,14,12,15,13,7,7,16,14,8,8,3,3,17,15,9,9,4,4,18,16,
%U 19,17,10,10,5,5,20,18,11,11,21,19,22,20,12,12,6,6,23,21,13,13,24,22,14,14,7,7,25,23,15,15,8,8,1,1,26,24,16,16
%N Ordinal transform of A175851.
%C Ordinal transform of the ordinal transform of the nextprime function, A151800(1..) = 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, ...
%H Antti Karttunen, <a href="/A304106/b304106.txt">Table of n, a(n) for n = 1..65537</a>
%F For all n >= 1, a(A008578(n)) = n.
%t A175851[n_] := If[!CompositeQ[n], 1, n - NextPrime[n, -1] + 1];
%t b[_] = 0;
%t a[n_] := a[n] = With[{t = A175851[n]}, b[t] = b[t] + 1];
%t Array[a, 105] (* _Jean-François Alcover_, Dec 21 2021 *)
%o (PARI)
%o up_to = 65537;
%o A151800(n) = nextprime(1+n);
%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o v304106 = ordinal_transform(ordinal_transform(vector(up_to,n,A151800(n))));
%o A304106(n) = v304106[n];
%Y Cf. A008578, A151800, A175851.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 09 2018